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A105385 Expansion of (1-x^2)/(1-x^5). 1
1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Binomial transform is A103311(n+1). Consecutive pair sums of A105384. Periodic {1,0,-1,0,0}.

LINKS

Table of n, a(n) for n=0..90.

Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1).

FORMULA

G.f.: (1+x)/(1 + x + x^2 + x^3 + x^4);

a(n) = sqrt(1/5 - 2*sqrt(5)/25)*cos(4*Pi*n/5 + Pi/10) + sqrt(5)*sin(4*Pi*n/5 + Pi/10)/5 + sqrt(2*sqrt(5)/25 + 1/5)*cos(2*Pi*n/5 + 3*Pi/10) + sqrt(5)*sin(2*Pi*n/5 + 3*Pi/10)/5.

a(n) = -(1/5)*((n mod 5) + ((n+2) mod 5) - ((n+3) mod 5) - ((n+4) mod 5)), with n >= 0. - Paolo P. Lava, Jun 01 2007

a(n) = A092202(n+1). - R. J. Mathar, Aug 28 2008

a(n) = a(n-1) - a(n-2) - a(n-3) - a(n-4); a(0)=1, a(1)=0, a(2)=-1, a(3)=0. - Harvey P. Dale, Mar 10 2013

MATHEMATICA

CoefficientList[Series[(1-x^2)/(1-x^5), {x, 0, 100}], x] (* or *) PadRight[{}, 100, {1, 0, -1, 0, 0}] (* or *) LinearRecurrence[{-1, -1, -1, -1}, {1, 0, -1, 0}, 100] (* Harvey P. Dale, Mar 10 2013 *)

CROSSREFS

Cf. A198517 (unsigned version).

Sequence in context: A127831 A164364 A198517 * A190227 A090626 A129569

Adjacent sequences:  A105382 A105383 A105384 * A105386 A105387 A105388

KEYWORD

sign,easy

AUTHOR

Paul Barry, Apr 02 2005

STATUS

approved

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Last modified February 26 21:27 EST 2020. Contains 332295 sequences. (Running on oeis4.)